celmech: A Python package for celestial mechanics

TL;DR

celmech is an open-source Python package that simplifies celestial mechanics calculations, allowing users to analyze resonances, develop analytical models, and interface with N-body simulations efficiently.

Contribution

The paper introduces celmech, a versatile Python package that integrates symbolic mathematics with celestial mechanics calculations and interfaces with REBOUND for N-body simulations.

Findings

Facilitates resonance analysis in planetary systems.

Enables development of minimal-term analytical models.

Seamlessly integrates with REBOUND for validation.

Abstract

We present celmech, an open-source Python package designed to facilitate a wide variety of celestial mechanics calculations. The package allows users to formulate and integrate equations of motion incorporating user-specified terms from the classical disturbing function expansion of the interaction potential between pairs of planets. The code can be applied, for example, to isolate the contribution of particular resonances to a system's dynamical evolution and develop simple analytical models with the minimum number of terms required to capture a particular dynamical phenomenon. Equations and expressions can be easily manipulated by leveraging the extensive symbolic mathematics capabilities of the sympy Python package. The celmech package is designed to interface seamlessly with the popular $N$-body code REBOUND to facilitate comparisons between calculation results and direct $N$-body integrations. The code is extensively documented and numerous example Jupyter notebooks illustrating its use are available online.